ShapeOfATsunami::usage="A simple model to measure the shape of a Tsunami or a tide is given by: = 2 - Where W[x] it is the height of the swell as a function of its position relative to a fixed point on the coast. Consider W[0] = 2. References: Zill, D.G.and Cullen, M.R. Differential Equations with Boundary-Value Problems. Dennis G. Zill. and Michael R. Cullen. Ed. Brooks/Cole: p.81, 1997; Personal.";
1
2
W
x
2
)
2
W
3
W
soln=DSolve==2-,W1[0]==2,W1[x],{x,0,10}
1
2
2
(W1'[x])
2
(W1[x])
3
(W1[x])
Out[]=
{{W1[x]2}}
2
Sech[x]
In[]:=
Plot[Evaluate[W1[x]/.soln],{x,0,10},PlotRangeAll]
Out[]=
As it approaches the coast, that is, x = 0, the height of the swell increases to 2. We know that near the coast the Tsunami slows down, the swell increases in height.